可逆逻辑电路的分类和多值量子逻辑电路的综合

项目名称： 可逆逻辑电路的分类和多值量子逻辑电路的综合

项目编号： No.61272175

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 杨国武

作者单位： 电子科技大学

项目金额： 82万元

中文摘要： 量子信息、量子计算是近20年的研究热点。本项目研究量子计算中可逆逻辑电路的分类和判定，多值量子逻辑电路的综合。主要是针对四个方面的研究：布尔函数的NP-N分类及判定；可逆逻辑电路的NP-N分类及判定；可逆逻辑电路的谱分类及判定；多值量子逻辑电路的综合。可逆逻辑电路的分类在电路设计中有广泛应用，如模块复用，可逆逻辑门库的构建，可逆逻辑电路综合等。多值量子系统拥有更强大的量子计算和信息处理能力。因此关于这些内容的研究非常重要。本项目首先用代数方法研究布尔函数的NP-N分类及判定问题，然后结合可逆逻辑电路的特性，研究它的NP-NP分类、谱分类及相关的判定；最后利用酉矩阵分解和李代数等，结合可逆逻辑电路综合的特点，研究多值量子逻辑电路门的一致性问题和综合问题，设计并实现优化的综合算法。

中文关键词： 可逆逻辑综合；多值量子电路；NP-N分类与等价判断；仿射分类与等价；多体量子纯态纠缠的判据

英文摘要： Quantum information and quantum computing are the hot research in recent twenty years. This proposal focuses on the classification and decision of reversible logic circuits, and synthesis of multi-valued quantum logic circuits in quantum computing. It includes four aspects: the NP-N classification and decision of Boolean functions; the NP-NP classification and decision of reversible logic circuits; the spectrum classification and decision of reversible logic circuits; synthesis of quantum logic circuits. The classifications have widespread use in design of circuits, such as reusability of moulds, construction of reversible logic libraries, and synthesis of reversible logic circuits. Therefore, the study on these problems is quite important. First, we will study the NP-N classification and the decision of Boolean functions based on algebra; then study the NP-NP classification, spectrum classification and the related decision of reversible logic circuits through their characters; finally, by using decomposition of unitary matrix and Li algebra, combining the characters of synthesis of reversible logic circuits, we will study the universal and synthesis problems of multi-valued quantum logic circuits, design optimal synthesis algorithms and implement them.

英文关键词： Reversible logic synthesis；multi-value quantum circuits；NP-N classification and equivalence criterion；affine classification and equivalence criterion；separability criterion for multipartite pure state